OFFSET
1,1
COMMENTS
Square terms are 36, 144, 576,... and the corresponding square roots are 6, 12, 24,... i.e. sequence A188158 (integer areas of primitive integer triangles).
Positive integers of the form (a^2-b^2)*(b^2-c^2) with integers a>b>c>=0. - Michael Somos, May 18 2013
REFERENCES
R. D. Carmichael, Diophantine Analysis, Wiley, 1915, p. 9.
EXAMPLE
a(21)=144 for x=1, y=4 and z=4 then the triangle sides are x+y = 5, z+x = 5 and y+z = 8, hence half-perimeter = p = x+y+z = 9 and Heron's formula is checked: area = sqrt(p*(p-5)*(p-5)*(p-8)) = sqrt(144) = 12.
36 = (4^2-2^2) * (2^2-1^2). 63 = (5^2-2^2) * (2^2-1^2) = (5^2-4^2) * (4^2-2^2)= (8^2-1^2) * (1^2-0^2). - Michael Somos, May 19 2013
MATHEMATICA
nmax = 25; mx = nmax (nmax + 2); Union[Reap[Do[a = (x + y + z)*x*y*z; If[a <= mx, Sow[a]], {x, 1, nmax}, {y, x, nmax}, {z, y, nmax}]][[2, 1]]]
CROSSREFS
KEYWORD
nonn
AUTHOR
Jean-François Alcover, Jun 06 2012
STATUS
approved